1/* 2 arrays.pl 3 4 @author Francois Fages 5 @email Francois.Fages@inria.fr 6 @license LGPL-2 7 8 @version 1.1.3 9 10 11 Multidimensional arrays with Array[Indices] functional notation and list conversions. 12 13 The indices are evaluated and can be expressions containing shorthands. 14 15*/ 16 17:- module( 18 arrays, 19 [ 20 array/1, 21 array/2, 22 23 cell/3, 24 cell/2, 25 op(100, yf, []), 26 27 array_lists/2, 28 array_list/2, 29 30 set_cell/3, 31 set_cell/2, 32 nb_set_cell/3, 33 nb_set_cell/2 34 ] 35 ).

multidimensional arrays with conversions to lists and Array[Indices] functional notation.

author

- Francois Fages

version

- 1.1.3

This module provides an implementation of multidimensional arrays by terms.

The array indices are integers starting at 1 and the dimension of an array is a list of integers.

array_list/2 (resp. array_lists/2) makes conversions between an array and a list (resp. of lists for multi-dimensional arrays), which can be used to initialize an array to a list of values.

?- array_lists(A, [[1, 2, 3], [4, 5, 6]]), array(A, Dim).
A = array(array(1, 2, 3), array(4, 5, 6)),
Dim = [2, 3].

Array cells are accessed by unification with predicate cell/3.

This module includes module comprehension.pl for bounded quantification and is compatible with attributed variables, clpfd and clpr libraries for creating arrays of constrained variables, and posting constraints on subscripted variables.

Array cells can also be modified by destructive assignment, backtrackable or not, with set_cell/3 and nb_set_cell/3.

?- array(A, [3]), cell(A, [2], v).
A = array(_, v, _).

?- array(A, [2, 3]), cell(A, [2,2], 3).
A = array(array(_, _, _), array(_, 3, _)).

?- array(A, [2, 3]), cell(A, [2], X).
A = array(array(_, _, _), array(_A, _B, _C)),
X = array(_A, _B, _C).

?- array_list(A, [2,3,4]), let([I=A[1],V=A[I]], writeln(a(I,V))).
a(2,3)
A = array(2, 3, 4).
  
?- array(A, [2, 3]), (set_cell(A, [1], 9) ; nb_set_cell(A, [2], 5); set_cell(A, [2,2],8)).
A = array(array(9, 9, 9), array(_, _, _)) ;
A = array(array(_, _, _), array(5, 5, 5)) ;
A = array(array(_, _, _), array(5, 8, 5)).

Array[Indices] functional notation defined here using multifile shorthand/3 predicate of library(comprehension) can be used in "in" and "where" conditions of comprehension metapredicates and in constraints of library(clp).

?- array(A, [5]), for_all([I in 1..5], A[I] #= I).
A = array(1, 2, 3, 4, 5).

116array(Array, Dimensions):- 117 expand(Array, A), 118 expand(Dimensions, D), 119 (var(A), (var(D) ; D=[N], var(N)) 120 -> 121 D=[N], 122 between(1, inf, N), 123 functor(A, array, N) 124 ; 125 array_rec(A, D)). 126 127array_rec(Array, Dimensions):- 128 (compound(Array) 129 -> 130 functor(Array, array, N), 131 Dimensions=[N|Tail], 132 for_all(I in 1..N, 133 let([Row=Array[I]], 134 (arrays:array_rec(Row, Tail) -> true ; Tail=[]))) 135 ; 136 nonvar(Dimensions), 137 Dimensions = [N | Tail], 138 nonvar(N), 139 functor(Array, array, N), 140 (Tail=[] 141 -> 142 true 143 ; 144 for_all(I in 1..N, let([Row=Array[I]], 145 (arrays:array_rec(Row, Tail)) -> true; Tail=[])))). 146 147 148 % CELL ACCESS

157cell(Array, I, _Term):- 158 must_be(compound, Array), 159 must_be(nonvar, I), 160 fail. 161 162cell(Array, [Ind | Indices], Term):- 163 !, 164 evaluate(Ind, I), 165 cell(Array, I, Row), 166 (Indices=[] 167 -> 168 Term=Row 169 ; 170 cell(Row, Indices, Term)). 171 172cell(Array, Expr, Term):- 173 evaluate(Expr, I), 174 arg(I, Array, Term).

181cell(ArrayIndices, Cell):- 182 must_be(nonvar, ArrayIndices), 183 ArrayIndices=Array[Indices], 184 cell(Array, Indices, Cell). 185 186 187 % SHORTHAND FUNCTIONAL NOTATION FOR ARRAY ACCESS 188 189 190:- multifile user:shorthand/3.

208array_list(Array, List):- 209 ( 210 array(Array) 211 -> 212 array_to_lists(Array, Lists), 213 flatten(Lists, List) 214 ; 215 Array =.. [array | List] 216 ).

225array_lists(Array, Lists):- 226 ( 227 array(Array) 228 -> 229 array_to_lists(Array, Lists) 230 ; 231 lists_to_array(Lists, Array) 232 ). 233 234 235array_to_lists(Array, List):- 236 Array =.. [array | Rows], 237 ( 238 (Rows=[R | _], array(R)) 239 -> 240 call_list(arrays:array_to_lists, Rows, List) 241 ; 242 List=Rows 243 ). 244 245lists_to_array(Lists, Array):- 246 must_be(list, Lists), 247 length(Lists, N), 248 array(Array, [N]), 249 for_all(I in 1..N, 250 exists([AI, LI], 251 (cell(Array, I, AI), nth1(I, Lists, LI), (is_list(LI) -> arrays:lists_to_array(LI, AI) ; LI=AI)) 252 ) 253 ). 254 255 256 257 258 259 % IMPERATIVE CELL ASSIGNMENT

267set_cell(Array, I, _Term):- 268 must_be(compound, Array), 269 must_be(nonvar, I), 270 fail. 271 272set_cell(Array, [I | Indices], Term):- 273 !, 274 (Indices=[] 275 -> 276 set_all_cells(Array, I, Term) 277 ; 278 cell(Array, I, Row), 279 set_cell(Row, Indices, Term)). 280 281set_cell(Array, Expr, Term):- 282 evaluate(Expr, I), 283 set_all_cells(Array, I, Term).

289set_cell(ArrayIndices, Cell):- 290 must_be(nonvar, ArrayIndices), 291 ArrayIndices=Array[Indices], 292 set_cell(Array, Indices, Cell). 293 294 295set_all_cells(Array, I, Term):- 296 arg(I, Array, A), 297 (compound(A), 298 functor(A, array, N) 299 -> 300 for_all([J in 1..N], arrays:set_all_cells(A, J, Term)) ; setarg(I, Array, Term) ).

311nb_set_cell(Array, I, _Term):- 312 must_be(compound, Array), 313 must_be(nonvar, I), 314 fail. 315 316nb_set_cell(Array, [I | Indices], Term):- 317 !, 318 (Indices=[] 319 -> 320 nb_set_all_cells(Array, I, Term) 321 ; 322 cell(Array, I, Row), 323 nb_set_cell(Row, Indices, Term)). 324 325nb_set_cell(Array, Expr, Term):- 326 evaluate(Expr, I), 327 nb_set_all_cells(Array, I, Term).

333nb_set_cell(ArrayIndices, Cell):- 334 must_be(nonvar, ArrayIndices), 335 ArrayIndices=Array[Indices], 336 nb_set_cell(Array, Indices, Cell). 337 338 339 340nb_set_all_cells(Array, I, Term):- 341 arg(I, Array, A), 342 (compound(A), 343 functor(A, array, N) 344 -> 345 for_all([J